Functions | Tyes of Correspondence | Partial Functions | Mathematical Structures | CS Connect 26

This video will discuss about functions in the context of mathematical structures. Along with practice problems, we will dive deep into functions.

00:00:00 Intro
00:00:26 Functions
00:04:13 Domain, Codomain, Range
00:05:00 Addition and multiplication of functions
00:09:41 Injective functions
00:14:02 Surjective functions
00:15:48 Bijective functions
00:16:39 Different types of Correspondence
00:20:05 Inverse functions
00:27:53 Composition of functions
00:32:56 Graphs of functions
00:35:25 Flooring and Ceiling functions
00:36:29 -Properties
00:39:16 Factorial function
00:40:15 Partial functions
00:42:30 Practice Problems
00:42:33 1. Determine whether f is a function from the set of all bit strings to the set of integers.
00:45:12 2. Find the domain and range of these functions.
00:48:04 3. Determine whether the function f:ZxZ to Z is onto.
00:50:20 4. Determine whether each of these functions is a bijection from R to R.
00:53:06 5. Find f(S) for the given function.
00:56:14 6. Find the composition of two given functions from R to R.
00:58:01 7. Show that the function f(x) = ax+b from R to R is invertible and find the inverse of f.
01:01:37 8. Find the inverse image of the following function.
01:05:44 9. Prove or disprove each of these statements about the floor and ceiling functions.
01:13:02 10. For each of these partial functions, determine its domain, codomain, domain of definition and the set of values for which it is undefined. Also, determine whether it is a total function.

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CS Connect File:
https://docs.google.com/presentation/...